Show instructions Question 7(1 point) What is the factored form of f(x)=5x^2-5x-60 f(x)=5(x+2)(x-6) b f(x)=5(x-4)(x+3) f(x)=5(x-2)(x+6) f(x)=5(x+4)(x-3) d

To find the factored form of the quadratic function $f(x)=5x^{2}-5x-60$, we need to factor the quadratic expression.<br /><br />The factored form of a quadratic expression is given by $(x-a)(x-b)$, where $a$ and $b$ are the roots of the quadratic equation.<br /><br />To find the roots, we can use the quadratic formula:<br />$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$<br /><br />In this case, the quadratic equation is $5x^{2}-5x-60=0$.<br /><br />Comparing this with the standard form of a quadratic equation $ax^2+bx+c=0$, we have:<br />$a=5$, $b=-5$, and $c=-60$.<br /><br />Substituting these values into the quadratic formula, we get:<br />$x=\frac{-(-5)\pm\sqrt{(-5)^2-4(5)(-60)}}{2(5)}$<br />$x=\frac{5\pm\sqrt{25+1200}}{10}$<br />$x=\frac{5\pm\sqrt{1225}}{10}$<br />$x=\frac{5\pm35}{10}$<br /><br />Therefore, the roots are $x=4$ and $x=-3$.<br /><br />So, the factored form of the quadratic function is:<br />$f(x)=5(x-4)(x+3)$<br /><br />Therefore, the correct answer is option b: $f(x)=5(x-4)(x+3)$.